# Quantum walk of a Bose-Einstein condensate in the Brillouin zone

## TL;DR

This paper proposes a feasible method to realize discrete-time quantum walks in the quasimomentum space of a spinor Bose-Einstein condensate using optical lattices and short pulses, enabling robust and long-range interaction simulations.

## Contribution

It introduces a natural scheme for quantum walks in the Brillouin zone with tunable boundary conditions and long-range interactions, avoiding off-resonant scattering issues.

## Key findings

- Implementation of quantum walks in quasimomentum space demonstrated
- Tunable twisted boundary conditions achieved naturally
- Potential for robust long-step quantum walk experiments

## Abstract

We propose a realistic scheme to implement discrete-time quantum walks in the Brillouin zone (i.e., in quasimomentum space) with a spinor Bose-Einstein condensate. Relying on a static optical lattice to suppress tunneling in real space, the condensate is displaced in quasimomentum space in discrete steps conditioned upon the internal state of the atoms, while short pulses periodically couple the internal states. We show that tunable twisted boundary conditions can be implemented in a fully natural way by exploiting the periodicity of the Brillouin zone. The proposed setup does not suffer from off-resonant scattering of photons and could allow a robust implementation of quantum walks with several tens of steps at least. In addition, onsite atom-atom interactions can be used to simulate interactions with infinitely long range in the Brillouin zone.